I am not a vet either - but it is surprising just what we humans and our canine family can actually do without.
If the vets suggest removing part of the duodenum, then it would seem to me that you are being dictated to by circumstance. Poor wee boy is not eating, has a fever, is in pain, is not enjoying life. You can't let him go on like this indefinitely. You are going to have to come to a decision and as the status quo seems not to be coming to a satisfactory outcome, you probably have no alternative.
Heartfelt sympathy from this side of the Pond - but whatever happens, you will know you have done your best for your Basenji. That is the best comfort.